Despite criticism over his remarks about the violence in Charlottesville, Virginia, Republican lawmakers appear to be still standing by President Donald Trump, The New York Times reported.

"If Republicans want to be in the majority, it's not a question of sticking from Trump, it's a question of accomplishing things," Rep. Tom Cole, R- Okla., told the newspaper shortly before Trump again claimed both white supremacists and counter-protesters were to blame for the violence in Charlottesville.

Cole added: "And most of those things require a presidential signature."

Some Republican lawmakers have avoided using Trump's name as they allude to his controversial remarks about the violence, the newspaper noted.

"We can have no tolerance for an ideology of racial hatred," Senate Majority Leader Mitch McConnel,l R-Ky., said on Wednesday.

And many appear willing to at least forget about his actions or remarks," said Cautham Rao, assistant professor of history at American University in an interview with Roll Call.

"This is a pattern that we see with the relationship between Trump and congressional Republicans going back to the campaign," Rao said.

"He is destroying the GOP one day at a time, one reckless statement and action at a time," said Sally Bradshaw, a longtime adviser to Jeb Bush who left the party over Trump. "Why would anyone consider supporting a political party when the leader of the party is anti-Semitic, anti-immigrant, anti-woman, and anti-black? He makes me sick."

Still, there remains strong disagreement over the impact of Trump's latest statement.

"We are a very inclusive party," said Glenn McCall, a South Carolina Republican national committeeman, who is African-American.

He agreed with Trump's assessment that both far-right and far-left agitators deserved equal blame.

"I don't think his comments will add any discontent among the workers, and the work that we're doing, to expand," McCall said.